Let $\, \overline {\! M}$ be a compact Riemannian manifold with sectional curvature $K_{\, \overline {\! M}}$
satisfying $1/5 K_{\, \overline {\! M}}\le 1$ (resp. $2\le K_{\, \overline {\! M}}10$), which can be
isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in $\, \overline {\! M}$. This extends Shen and Xu's result for ${1\over 4}$-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson–Simons conjecture.
Keywords:
overline compact riemannian manifold sectional curvature overline satisfying overline resp overline which isometrically immersed hypersurface euclidean space resp unit euclidean sphere there exist stable compact minimal submanifolds overline extends shen xus result pinched riemannian manifolds suggests modified version well known lawson simons conjecture
Affiliations des auteurs :
Ze-Jun Hu
1
;
Guo-Xin Wei
1
1
Department of Mathematics Zhengzhou University Zhengzhou 450052, P.R. China
Ze-Jun Hu; Guo-Xin Wei. On the nonexistence of stable minimal submanifolds
and the Lawson–Simons conjecture. Colloquium Mathematicum, Tome 96 (2003) no. 2, pp. 213-223. doi: 10.4064/cm96-2-6
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title = {On the nonexistence of stable minimal submanifolds
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